14 citations · 45 across the 16 of their papers we have counts for
6 papers · 1 filter
Isometric and affine copies of a set in volumetric Helly results
John A. Messina, Pablo Soberón
We show that for any compact convex set in and any finite family of convex sets in , if the intersection of every sufficiently small…
A mélange of diameter Helly-type theorems
Travis Dillon, Pablo Soberón
A Helly-type theorem for diameter provides a bound on the diameter of the intersection of a finite family of convex sets in given some information on the diameter of…
Balanced convex partitions of lines in the plane
Alexander Xue, Pablo Soberón
We prove an extension of a ham sandwich theorem for families of lines in the plane by Dujmović and Langerman. Given two sets of lines each in the plane, we prove that it…
Non-commutative groups as prescribed polytopal symmetries
Alexandru Chirvasitu, Frieder Ladisch, Pablo Soberón
We study properties of the realizations of groups as the combinatorial automorphism group of a convex polytope. We show that for any non-abelian group with a central involution…
Helly's Theorem: New Variations and Applications
Nina Amenta, Jesús A. De Loera, Pablo Soberón
This survey presents recent Helly-type geometric theorems published since the appearance of the last comprehensive survey, more than ten years ago. We discuss how such theorems con…
Quantitative Tverberg, Helly, & Carathéodory theorems
J. A. De Loera, R. N. La Haye, D. Rolnick +1
This paper presents sixteen quantitative versions of the classic Tverberg, Helly, & Caratheodory theorems in combinatorial convexity. Our results include measurable or enumerable i…